One of the key parameters distinguishing accelerometers is offset performance, both initial and over time and temperature. For example, lateral micromachined accelerometers having a movable mass typically employ multiple mass suspensions affixed to a substrate and positioned outside of the mass' boundaries. Sensing fingers that measure movement of the mass relative to the sensing fingers are typically also affixed to the substrate outside of the mass' boundaries, for example, around the mass. If the chip is subject to stress, such as that which may arise from the assembly process and from thermal variations, the relative position of the mass and the sensing fingers may change. For example, normal process variations cause differences between the spring constants of the springs connected between these anchors and the movable mass. If the distance between the anchors changes, the difference in the spring constants can cause an unequal displacement of the mass relative to the anchors, which can move the mass relative to the sensing fingers and be interpreted as an offset.
Likewise, the sensor material may have internal stresses as a result of the manufacturing process, which can also cause an offset. For example, if the movable mass material were under tension or compression, the springs could be displaced unequally, which can move the mass relative to the sensing fingers and be interpreted as an offset. This offset is typically corrected by laser trimming resistors in the signal conditioning circuitry, or by adjusting the offset by one of several methods once the part has been packaged.
Micromachined accelerometers often include electromechanical components that are mechanically attached to the substrate. Some of these components are mobile with respect to other components, or to the substrate. Others are ideally immobile with respect to the substrate. One example of immobile components is the fixed sensing fingers of a lateral accelerometer.
Components are typically connected to the substrate by an “anchor” formed by one or more manufacturing processes. If the component suspended by this anchor is large compared to the dimensions of the anchor, the anchor may be subject to significant amounts of torque or bending moment in the application environment. This torque or bending moment may be caused, for example, by an inertial response to a mechanical event such as an acceleration or shock or by an electrostatic force between the finger and its environment such as an electrostatic force generated by a voltage applied during normal operation or a voltage arising from an electrostatic discharge event. A small amount of torsional rotation or bending displacement of the anchor can cause a large deflection of the suspended structure.
The fixed sensing fingers are not infinitely rigid. The net deflection at the tip of a finger is a combination of the bending of the finger and the bending and twisting of the anchor. Depending on the dimensions and mechanical properties of the finger and the anchor, the twisting and/or bending of the anchor can be a significant, and even the dominant term contributing to the deflection of the tip of the finger.
The displacement of an accelerometer proof mass on a spring as a result of input acceleration is given by 1/w0^2, where w0 is 2*pi*f0, and f0 is the resonant frequency. An accelerometer with a high resonant frequency has a low displacement per unit acceleration. Thus, any error equivalent to a displacement of the sensor causes a larger equivalent offset in units of acceleration on higher resonant frequency sensors. For example, the displacement of a fixed finger, relative to the sensor due to die stress causes greater apparent offset in high resonant frequency devices.
Another cause of offset is displacement of the sensor relative to the substrate in response to stimuli other than acceleration, such as die stress. In a single-axis accelerometer, if there are two anchors connecting the springs to the substrate located along the axis of sensitivity, the offset due to die stress is proportional to the distance between the anchors. Normal manufacturing variations cause differences in the spring constants of the springs connected to each anchor. When die stress changes the separation between the anchors, the difference in spring constants causes a displacement of the sensor relative to the substrate, which is interpreted as an offset. Since the change in separation between the anchors is proportional to the distance between the anchors for a given die stress, the offset error due to this term is also proportional to the distance between the anchors:
The relationship between anchor separation (sep), resonant frequency (f0), and offset (OS) is given as:OS˜sep*f0^2.